Before we can discuss the classical quadratic sieve and design its quantum variant, some preliminaries and definitions are given in this section. Linear algebra is an essential mathematical tool for quantum mechanics. Linear operators allow us to represent quantum mechanical operators as matrices and wave functions as vectors on some linear vector space. We assume that the reader is familiar with the notation of quantum mechanics; otherwise, reader can refer to quantum computational, quantum computing [1]} [2]} and number theory [3]}.
